The Wiener Index of the Composition of Two Planar Graphs

The Wiener index, is the first, and also one of the most important topological indices of chemical graphs. Furthermore, there are many situations in communication, facility location, cryptology, architecture etc, where the Wiener index of the corresponding graph or the average distance is of great interest. One of the problems, for example, is to find a spanning tree with minimum average distance. In this paper we present the notion of the composition of two planar graphs, through some examples and, we will focus to calculate the Wiener index for the composition of two cycle planar graphs W(C_n1 °C_n2 ) and the Wiener index for the composition of cycle planar graph and path planar graph W(C_n1°P_n2 ), using oar´s theorem.